Class CBSE Class 12 Mathematics Matrices and Determinants Q #745
KNOWLEDGE BASED
APPLY
1 Marks 2024 MCQ SINGLE
If \(\begin{bmatrix}x+y&2\\ 5&xy\end{bmatrix}=\begin{bmatrix}6&2\\ 5&8\end{bmatrix},\) then the value of \((\frac{24}{x}+\frac{24}{y})\) is:
(A) 7
(B) 6
(C) 8
(D) 18
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Step-by-Step Solution

Given the matrix equation:

\[\begin{bmatrix}x+y&2\\ 5&xy\end{bmatrix}=\begin{bmatrix}6&2\\ 5&8\end{bmatrix}\]

From the equality of matrices, we have two equations:

  1. \(x + y = 6\)
  2. \(xy = 8\)

We need to find the value of \(\frac{24}{x} + \frac{24}{y}\). We can rewrite this expression as:

\[\frac{24}{x} + \frac{24}{y} = 24\left(\frac{1}{x} + \frac{1}{y}\right) = 24\left(\frac{x+y}{xy}\right)\]

Now, substitute the values of \(x+y\) and \(xy\) from the equations above:

\[24\left(\frac{6}{8}\right) = 24\left(\frac{3}{4}\right) = 6 \times 3 = 18\]

Correct Answer: 18

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concept of equality of matrices and solve the resulting equations to find the values of x and y, and then substitute those values into the given expression.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of matrix equality and how to solve simultaneous equations derived from it.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of matrix equality and their ability to solve related algebraic equations, which aligns with textbook knowledge.

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